THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY

By Colin Carroll, Adam Jacob, Conor Quinn, Robin Walters. 2008

61 citations recorded by the source corpus.

We discuss the isoperimetric problem in planes with density. In particular, we examine planes with generalized curvature zero. We solve the isoperimetric problem on the plane with density e x , as well as on the plane with density r p for p

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/e4e52f3cca4c038c201d6f6c976cd88987d3c8b2

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In Applied Mathematics

1. Antonio Cañete
2. Michele Miranda Jr.
3. Davide Vittone
4. Luigi Ambrosio
5. R. Korte
6. Simone Di Marino

In Astronomy and Astrophysics

1. Michele Miranda Jr.
2. Davide Vittone

Citations in the corpus

• Sharp isoperimetric inequalities via the ABP method (2013, unknown): “On the one hand, Carroll– Jacob–Quinn–Walters [13] showed that when α < − 2 all minimizers are R 2 \ B r ( 0 ) , r > 0, and that when − 2 ≤ α < 0 minimizers do not exist.”
• Some Isoperimetric Problems in Planes with Density (2009, methodology): “10 Let us consider the plane R(2) endowed with the density f(x, y) = e introduced in [10], where it is proved (see Corollary 4.”